Back radiation and the 2nd Law of Thermodynamics.

Simplified thermodynamic system.
If Each ball=40J

Then without the Green box the Blue box would receive and emit 150J/sec and working back from S.B, emitted E=T^4, has a temp of ~ 196KWith the Green box returning and extra 10J/sec to the Blue box as back radiation it emits 160J/sec and has a temp of 200K.
The Green box receiving and emitting 40J/sec has a temp of ~141K

For the context and further explanation please see the full post.

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In both the Evolution-Creationist debate, and the AGW-‘skeptic’ conflict the 2nd Law of thermodynamics is invoked as a strong refutation of the central theory.

In each case the 2nd Law is modified to refer more directly to the issue. In both cases the error is conceptually the same.
Creationists frame the 2nd Law as an absolute prohibition of order ever increasing, ordered systems must always become more dis-ordered. Which they then claim makes it impossible to get from molecules to an organism. Ignoring the fact that their own conception, gestation and growth to adulthood requires that to have happened.

AGW ‘skeptics‘ invoke the second law as an absolute block on a cooler object contributing any energy (order in the Creationist version) to a hotter object.

Despite the low regard both groups seem to hold of science, they  recognise that Thermodynamics is a key and fundamental aspect of scientific understanding.
It is the LAW !
So they correctly infer that if a hypothesis did contradict thermodynamics, it would fail at the first hurdle of being consistent with the most fundamental aspect of our understanding of the material universe.

This post is inspired in part by the recent Eli Rabbet attempt to simplify the physics to show how back radiation will warm an object.  The Green Plate Effect.Which prompted a long and byzantine comments thread were the idea that the 2nd Law invalidated AGW proved to be alive and well. Or at least a zombie that returns to walk again however many times it gets put down.

The simplifications Eli introduced with his Green Plate Effect became a target for objections, the argument spinning off into emission spectra and edge effects. Despite that, I intend to simplify even further.

1)-All inputs and outputs of energy are quantised into fixed amounts.

2)-All directions of emissions are quantised into a 2D plane and the 4 orthagonal directions; N. S. E. W.

3)-The boxes (plates, molecules, planets) are perfect black-bodies with zero albedo. they absorb and emit at all energies.

4)-Events that are siultaneous and continuous are depicted as staggered in time and rate.

To the objection this makes the setup so UNphysical it is useless as a model of energy exchange I would contend that it is not unlike the situation with 2 isolated molecules.

The restriction in directions is a geometrical simplification making it easier to visualise, but has no effect on the outcome, the all directions in 3D case makes no difference if the amounts emitted and absorbed are the same.
Adjustments for albedo/reflection can be made, but unless you invent Maxwell’s Demon; if a box can emit a frequency then it must also absorb it.
In similar fashion, the different timings and rates make it easier to see what is happening, and are intended to hint at least to the different spectra of the energy exchanged. But that makes no difference to the overall accounting of energy in = energy out for the whole system and the subsidiary parts of it.

Example 1
In this instance the ‘Black box’ is in thermodynamic equilibrium. There are 15 quanta of energy entering it every time period, and 15 quanta leaving it, lost to the 2.725K of deep space. Everything in accordance with the 2nd Law. The amount and spectra of the emissions indicate a temperature of about 196K.

Example 2.
In this instance the ‘Black box’ is in thermodynamic equilibrium. There are 15 quanta of energy entering it every time period, and 15 quanta leaving it, lost to the 2.725K of deep space. Everything in accordance with the 2nd Law. Although the more perceptive may have noticed that the spectra of the emissions is not a single, simple Stefan-Boltzmann spectra, although the amount of energy is the same and indicates an average temperature for the black box of 196K.

Example 3.
Here we see inside the ‘Black box 1’ showing the situation with just one absorbing/emitting Blue box object, it is the duplicate of example 1 with the Blue box at 196K and emitting a SB spectrum consistent with that.

Example 4.
This is inside the ‘Black box’ in example 2. The 25% of the Blue box emissions are absorbed by the Green box, so it emits that amount of energy in thermodynamic balance. 25% of which is re-absorbed by the blue box.

The result is that instead of receiving and emitting 15 quanta of energy per unit time, one quanta is not lost to space but recycled from the Green box so that the Blue box receives 16 quanta per unit time. No extra energy has been created, it has just been shuffled between objects. There are STILL 15 Quanta lost to deep space per unit time by the total system. Although the Blue box is actually absorbing/emitting 16 quanta, giving it a higher temperature of 200K. The Green box has a temperature of 141K so the emissions of the total system are a mix of SB spectra of those temperatures.

I think this is the underlying method that allows cosmologists to detect and determine the temperature on exo-planets. And Physical chemists to determine the energy stage of molecules in a mixture.

So that is how, and why an adjacent cooler object will cause an object with a continuous energy input to cool more slowly because it receives an extra input (part of its own output) resulting in it having a higher temperature or energy content than if the adjacent object (plate, planet molecule) was not there.

Comments welcome on any errors or improvements that you can suggest.